Uplink connections are typically used to connect the switch to a higher level switch, that is more powerful and closer to the backbone.
On basic switch models, the regular ports are MDIX ports, meant to connect directly to a PC. The Uplink port is then an MDI port, which can connect (with a straight cable) to an MDIX port on a different switch. Often the highest numbered port (8, 16, or 24 for instance) has one MDIX port in the regular set and an MDI uplink next to it, but you can only use one of these two.
You can use a crossover cable to connect MDIX to MDIX or MDI to MDI port.
On more modern switches, ports are often MDI/MDIX autosensing and this reason for existence of uplink ports has passed (all Gigabit Ethernet has this, and many 100 Mbit Ethernet).
In the mean time, however, switch models have come into being which have faster speed uplink ports. For instance, 10 Mbit switches with 1 or 2 100 Mbit ports to connect to the core network, or these days 100 Mbit switches with a few Gigabit ports.